Topic modeling with a tree-based prior has been used for a variety of applications be- cause it can encode correlations between words that traditional topic modeling cannot. How- ever, its expressive power comes at the cost of more complicated inference. We extend the SPARSELDA (Yao et al., 2009) inference scheme for latent Dirichlet allocation (LDA) to tree-based topic models. This sampling scheme computes the exact conditional distri- bution for Gibbs sampling much more quickly than enumerating all possible latent variable assignments. We further improve performance by iteratively refining the sampling distribution only when needed. Experiments show that the proposed techniques dramatically improve the computation time.